Don't listen when people say you're not a real Dj because you don't use vinyl. (I've never mixed with vinyl.)
Don't listen when they say using a computer means you're not really mixing. (I use my computer every gig I can - i have 26,000+ songs on it, so I'm always ready when the crowd goes in a different direction that I expect.)
Don't listen when they say if you use the "sync" button you're a poser. (i use the sync button, especially when I am mixing with 4 decks at once - BUT I also know how to beat-match - and you better know how, too.)
As long as you know what you are doing, have a good library of music, can read a crowd AND constantly work at getting better - you are a dj.